# yI0-xI1.R
# Philips, Andrew Q. "How to Avoid Incorrect Inference (While Gaining Correct Ones) in Dynamic Models". Forthcoming at Political Science Research and Methods. 
# andrew.philips@colorado.edu
# 2/9/21
#
# Figures produced in this R script:
#   --Main document, Figure 3: "yi0-xi1.pdf"
#   --SI, Figure 7: "yi0-xi1-evar5.pdf"
#   --SI, Figure 8: "yi0-xi1-MSE.pdf"
#   --SI, Figure 9: "yi0-xi1-MSE-evar5.pdf"
# -----------------------------------

rm(list = ls())
setwd("~/Dropbox/My_Folder/Papers-Projects/Wlezien-Enns-PSRM/Final-Feb2021/scripts/")
# -----------------------------------
library(dynamac)
library(nlWaldTest)
library(ggplot2)
library(grid)
library(gridExtra)
library(dplyr)

set.seed(5439277)
# -------------------------------------------------------------
# EXPERIMENT 2: Y ~ I(0), X ~ I(1)
sims = 2000 # no. sims
ar.param <- seq(0, 0.95, by = 0.05) # autoregression in Y
N <- c(50, 250, 1000) # number of obs
e.var <- c(1, 5) # error variance in Y

container.ardl <- matrix(NA, nrow = sims*length(ar.param)*length(N)*length(e.var), ncol = 10) # null matrix to hold output
# cols = sims, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
container.ecm <- matrix(NA, nrow = sims*length(ar.param)*length(N)*length(e.var), ncol = 10) # null matrix to hold output
# cols = sims, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
container.ldv <- matrix(NA, nrow = sims*length(ar.param)*length(N)*length(e.var), ncol = 10) # null matrix to hold output
# cols = sims, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, e.var
container.static <- matrix(NA, nrow = sims*length(ar.param)*length(N)*length(e.var), ncol = 7) # null matrix to hold output
# cols = sims, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, e.var
# -------------------------------------------------------------

row <- 1
prog <- txtProgressBar(min = 0, max = sims, style = 3)
for (s in 1:sims) {
  for (ar.y in ar.param) {
    for (n in N) {
      for (ev in e.var) {
        setTxtProgressBar(prog, value = s)
        # create Y
        if (ar.y == 0) {
          y <- rnorm(n + 100, sd = sqrt(ev))
        } else {
          y <- arima.sim(n = (n + 100), list(ar = c(ar.y)), innov = rnorm(n = (n + 100), sd = sqrt(ev)))
        }
        # create X
        x <- cumsum(rnorm(n + 100))
        # ARDL model:
        res.ardl <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)] + lshift(x, 1)[101:length(x)])
        # ECM model:
        res.ecm <- lm(dshift(y)[101:length(y)] ~ lshift(y, 1)[101:length(y)] + dshift(x)[101:length(x)] + lshift(x, 1)[101:length(x)])
        # LDV model
        res.ldv <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)])
        # static model
        res.static <- lm(y[101:length(y)] ~ x[101:length(x)])
      
        # grab QOI (FORALL): ----
        container.ardl[row, 1] <- container.ecm[row, 1] <- container.ldv[row, 1] <- container.static[row, 1] <- s
        container.ardl[row, 2] <- container.ecm[row, 2] <- container.ldv[row, 2] <- container.static[row, 2] <- ar.y
        container.ardl[row, 3] <- container.ecm[row, 3] <- container.ldv[row, 3] <- container.static[row, 3] <- n
        container.ardl[row, 10] <- container.ecm[row, 10] <- container.ldv[row, 10] <- container.static[row, 7] <- ev
      
        # QOI (ARDL)
        container.ardl[row, 4] <- coef(res.ardl)[3] # beta.x
        container.ardl[row, 5] <- confint.default(res.ardl, parm = c(3), level = 0.95)[2] # UL
        container.ardl[row, 6] <- confint.default(res.ardl, parm = c(3), level = 0.95)[1] # LL
        # LR effects (ARDL)
        lrm <- nlConfint(res.ardl, "(a[3] + a[4])/(1-a[2])", level = 0.95)
        container.ardl[row, 7] <- lrm[1] # LRM
        container.ardl[row, 8] <- lrm[3] # LRM UL
        container.ardl[row, 9] <- lrm[2] # LRM LL
      
        # QOI (ECM)
        container.ecm[row, 4] <- coef(res.ecm)[3] # beta.d.x
        container.ecm[row, 5] <- confint.default(res.ecm, parm = c(3), level = 0.95)[2] # UL
        container.ecm[row, 6] <- confint.default(res.ecm, parm = c(3), level = 0.95)[1] # LL
        # LR effects (ECM)
        lrm <- nlConfint(res.ecm, "(a[4])/(-a[2])", level = 0.95)
        container.ecm[row, 7] <- lrm[1] # LRM
        container.ecm[row, 8] <- lrm[3] # LRM UL
        container.ecm[row, 9] <- lrm[2] # LRM LL
      
        # QOI (LDV)
        container.ldv[row, 4] <- coef(res.ldv)[3]
        container.ldv[row, 5] <- confint.default(res.ldv, parm = c(3), level = 0.95)[2] # UL
        container.ldv[row, 6] <- confint.default(res.ldv, parm = c(3), level = 0.95)[1] # LL
        # LR effects (LDV)
        lrm <- nlConfint(res.ldv, "(a[3])/(1-a[2])", level = 0.95)
        container.ldv[row, 7] <- lrm[1] # LRM
        container.ldv[row, 8] <- lrm[3] # LRM UL
        container.ldv[row, 9] <- lrm[2] # LRM LL
      
        # QOI (static)
        container.static[row, 4] <- coef(res.static)[2]
        container.static[row, 5] <- confint.default(res.static, parm = c(2), level = 0.95)[2] # UL
        container.static[row, 6] <- confint.default(res.static, parm = c(2), level = 0.95)[1] # LL
      
        row <- row + 1
      } # close error var loop
    } # close N loop
  } # close AR.y loop
} # close sim loop

# save data:
#save.image("scenario-yi0-xi1-data.RData")
#load("scenario-yi0-xi1-data.RData")

# Create rejection rates and label:
container.ardl <- as.data.frame(container.ardl)
# cols = sim, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ardl) <- c("sims", "ar.param.Y", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.ecm <- as.data.frame(container.ecm)
# cols = sim, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ecm) <- c("sims", "ar.param.Y", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.ldv <- as.data.frame(container.ldv)
# cols = sim, ar.param.Y, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ldv) <- c("sims", "ar.param.Y", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.static <- as.data.frame(container.static)
# cols = sim, ar.param.Y, N, Beta.x, UL.beta.x, e.var
colnames(container.static) <- c("sims", "ar.param.Y", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "e.var")

# proportion false rejection
container.ardl$reject.beta.x <- ifelse(container.ardl$Beta.x.ll > 0 | container.ardl$Beta.x.ul < 0, 1, 0)
container.ecm$reject.beta.x <- ifelse(container.ecm$Beta.x.ll > 0 | container.ecm$Beta.x.ul < 0, 1, 0)
container.ldv$reject.beta.x <- ifelse(container.ldv$Beta.x.ll > 0 | container.ldv$Beta.x.ul < 0, 1, 0)
container.static$reject.beta.x <- ifelse(container.static$Beta.x.ll > 0 | container.static$Beta.x.ul < 0, 1, 0)

# coverage of LRM:
container.ardl$reject.lrm <- ifelse(container.ardl$LR.x.LL > 0 | container.ardl$LR.x.UL < 0, 1, 0)
container.ecm$reject.lrm <- ifelse(container.ecm$LR.x.LL > 0 | container.ecm$LR.x.UL < 0, 1, 0)
container.ldv$reject.lrm <- ifelse(container.ldv$LR.x.LL > 0 | container.ldv$LR.x.UL < 0, 1, 0)

# squared error:
container.ardl$sqerr.beta <- (container.ardl$Beta.x - 0)^2
container.ecm$sqerr.beta <- (container.ecm$Beta.x - 0)^2
container.ldv$sqerr.beta <- (container.ldv$Beta.x - 0)^2
container.static$sqerr.beta <- (container.static$Beta.x - 0)^2
container.ardl$sqerr.lrm <- (container.ardl$LR.x - 0)^2
container.ecm$sqerr.lrm <- (container.ecm$LR.x - 0)^2
container.ldv$sqerr.lrm <- (container.ldv$LR.x - 0)^2

# collapse everything down:
container.collapse.ardl <- container.ardl %>%
  group_by(ar.param.Y, Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x),
    reject.lrm = mean(reject.lrm),
    mse.beta.x = mean(sqerr.beta),
    mse.lrm = median(sqerr.lrm))

container.collapse.ecm <- container.ecm %>%
  group_by(ar.param.Y, Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x), 
    reject.lrm = mean(reject.lrm),
    mse.beta.x = mean(sqerr.beta),
    mse.lrm = median(sqerr.lrm))

container.collapse.ldv <- container.ldv %>%
  group_by(ar.param.Y, Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x), 
    reject.lrm = mean(reject.lrm),
    mse.beta.x = mean(sqerr.beta),
    mse.lrm = median(sqerr.lrm))

container.collapse.static <- container.static %>%
  group_by(ar.param.Y, Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x),
    mse.beta.x = mean(sqerr.beta))

# separate by T:
container.collapse.ardl.50 <- subset(container.collapse.ardl, Time == 50)
container.collapse.ardl.250 <- subset(container.collapse.ardl, Time == 250)
container.collapse.ardl.1000 <- subset(container.collapse.ardl, Time == 1000)
container.collapse.ecm.50 <- subset(container.collapse.ecm, Time == 50)
container.collapse.ecm.250 <- subset(container.collapse.ecm, Time == 250)
container.collapse.ecm.1000 <- subset(container.collapse.ecm, Time == 1000)
container.collapse.ldv.50 <- subset(container.collapse.ldv, Time == 50)
container.collapse.ldv.250 <- subset(container.collapse.ldv, Time == 250)
container.collapse.ldv.1000 <- subset(container.collapse.ldv, Time == 1000)
container.collapse.static.50 <- subset(container.collapse.static, Time == 50)
container.collapse.static.250 <- subset(container.collapse.static, Time == 250)
container.collapse.static.1000 <- subset(container.collapse.static, Time == 1000)

# plot: -------------------------------------------
# for these plots, e.var == 1
summary(subset(container.collapse.static, e.var == 1, select = reject.beta.x)) # figure out breaks
# SR, T = 50
p1 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.50, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.75)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# SR, T = 250
p2 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.250, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.75)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# SR, T = 1000
p3 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.1000, e.var == 1), aes(x = ar.param.Y, y = reject.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.75)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

# LR, T = 50
p4 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.75)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 250
p5 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.75)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 


# LR, T = 1000
p6 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 1), aes(x = ar.param.Y, y = reject.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.75)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

pdf("yi0-xi1.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, p3, p4, p5, p6, ncol = 3)
dev.off()


# plot: -------------------------------------------
# for these plots, e.var == 5
summary(subset(container.collapse.static, e.var == 5, select = reject.beta.x)) # figure out breaks
# SR, T = 50
p1 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.50, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.8)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

# SR, T = 250
p2 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.250, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.8)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

# SR, T = 1000
p3 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.1000, e.var == 5), aes(x = ar.param.Y, y = reject.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.8)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

# LR, T = 50
p4 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.8)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

# LR, T = 250
p5 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.8)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 


# LR, T = 1000
p6 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 5), aes(x = ar.param.Y, y = reject.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.8)) + geom_hline(yintercept = 0.05, color = "black", size = 1) +
  ylab("Proportion Rejected") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
        text = element_text(size=10), # size of axis numbers
        plot.title = element_text(size = 15)) 

pdf("yi0-xi1-evar5.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, p3, p4, p5, p6, ncol = 3)
dev.off()

# ---- MSE, evar = 1 -------
# using mean square error for SR effects, and median sq error for LR
summary(subset(container.collapse.static, e.var == 1, select = mse.beta.x)) # figure out breaks
# SR, T = 50
p1 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.50, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.25)) +
  ylab("MSE") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# SR, T = 250
p2 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.250, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.25)) +
  ylab("MSE") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# SR, T = 1000
p3 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.1000, e.var == 1), aes(x = ar.param.Y, y = mse.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.25)) +
  ylab("MSE") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 50
p4 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.25)) +
  ylab("Median Sq Error") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 250
p5 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.25)) +
  ylab("Median Sq Error") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 1000
p6 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 1), aes(x = ar.param.Y, y = mse.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 0.25)) +
  ylab("Median Sq Error") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

pdf("yi0-xi1-MSE.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, p3, p4, p5, p6, ncol = 3)
dev.off()
# --------------------------------

# ------- MSE, evar = 5 --------
summary(subset(container.collapse.static, e.var == 5, select = mse.beta.x)) # figure out breaks
p1 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.50, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 1.1)) +
  ylab("MSE") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# SR, T = 250
p2 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.250, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 1.1)) +
  ylab("MSE") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# SR, T = 1000
p3 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  geom_line(data = subset(container.collapse.static.1000, e.var == 5), aes(x = ar.param.Y, y = mse.beta.x), color = "#fdbe85", size = 1.7, lty = 'dotdash') +
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 1.1)) +
  ylab("MSE") + xlab("Autoregression in Y") + ggtitle("Short-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 50
p4 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.50, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.50, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.50, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 1.1)) +
  ylab("Median Sq Error") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=50") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 250
p5 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.250, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.250, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.250, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 1.1)) +
  ylab("Median Sq Error") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=250") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

# LR, T = 1000
p6 <- ggplot() + 
  geom_line(data = subset(container.collapse.ardl.1000, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color = "#a63603", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ecm.1000, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color =  "#e6550d", size = 1.7, lty = 'solid') + 
  geom_line(data = subset(container.collapse.ldv.1000, e.var == 5), aes(x = ar.param.Y, y = mse.lrm), color = "#fd8d3c", size = 1.7, lty = 'dashed') + 
  scale_x_continuous(breaks = seq(0,.95,.15)) +  scale_y_continuous(limits = c(0, 1.1)) +
  ylab("Median Sq Error") + xlab("Autoregression in Y") + ggtitle("Long-Run, T=1000") +
  theme(panel.background = element_rect(fill = NA), panel.grid.major = element_line(colour = "grey88"), panel.ontop = FALSE, # customize axis lines in background
    text = element_text(size=10), # size of axis numbers
    plot.title = element_text(size = 15)) 

pdf("yi0-xi1-MSE-evar5.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, p3, p4, p5, p6, ncol = 3)
dev.off()
# --------------------------------